Mostrando recursos 1 - 20 de 1.015

Athreya, Siva; Röllin, Adrian
We consider a particular respondent-driven sampling procedure governed by a graphon. Using a specific clumping procedure of the sampled vertices, we construct a sequence of sparse graphs. If the sequence of the vertex-sets is stationary, then the sequence of sparse graphs converges to the governing graphon in the cut-metric. The tools used are a concentration inequality for Markov chains and the Stein-Chen method.

Jakubowski, Adam
The $S$ topology on the Skorokhod space was introduced by the author in 1997 and since then it has proved to be a useful tool in several areas of the theory of stochastic processes. The paper brings complementary information on the $S$ topology. It is shown that the convergence of sequences in the $S$ topology admits a closed form description, exhibiting the locally convex character of the $S$ topology. Morover, it is proved that the $S$ topology is, up to some technicalities, finer than any linear topology which is coarser than Skorokhod’s $J_1$ topology. The paper contains also definitions of...

Deya, Aurélien; Schott, René
We pursue the investigations initiated by Donati-Martin [9] and Effros-Popa [10] regarding the multiplication issue in the chaoses generated by the $q$-Brownian motion ($q\in (-1,1)$), along two directions: $(i)$ We provide a fully-stochastic approach to the problem and thus make a clear link with the standard Brownian setting; $(ii)$ We elaborate on the situation where the kernels are given by symmetric functions, with application to the study of the $q$-Brownian martingales.

Ding, Jian; Goswami, Subhajit
We consider the branching random walk $\{\mathcal R^N_z: z\in V_N\}$ with Gaussian increments indexed over a two-dimensional box $V_N$ of side length $N$, and we study the first passage percolation where each vertex is assigned weight $e^{\gamma \mathcal R^N_z}$ for $\gamma >0$. We show that for $\gamma >0$ sufficiently small but fixed, the expected FPP distance between the left and right boundaries is at most $O(N^{1 - \gamma ^2/10})$.

Ding, Jian; Goswami, Subhajit
We consider the branching random walk $\{\mathcal R^N_z: z\in V_N\}$ with Gaussian increments indexed over a two-dimensional box $V_N$ of side length $N$, and we study the first passage percolation where each vertex is assigned weight $e^{\gamma \mathcal R^N_z}$ for $\gamma >0$. We show that for $\gamma >0$ sufficiently small but fixed, the expected FPP distance between the left and right boundaries is at most $O(N^{1 - \gamma ^2/10})$.

Ding, Jian; Goswami, Subhajit
We consider the branching random walk $\{\mathcal R^N_z: z\in V_N\}$ with Gaussian increments indexed over a two-dimensional box $V_N$ of side length $N$, and we study the first passage percolation where each vertex is assigned weight $e^{\gamma \mathcal R^N_z}$ for $\gamma >0$. We show that for $\gamma >0$ sufficiently small but fixed, the expected FPP distance between the left and right boundaries is at most $O(N^{1 - \gamma ^2/10})$.

Evans, Steven N.; Wakolbinger, Anton
The trie-based radix sort algorithm stores pairwise different infinite binary strings in the leaves of a binary tree in a way that the Ulam-Harris coding of each leaf equals a prefix (that is, an initial segment) of the corresponding string, with the prefixes being of minimal length so that they are pairwise different. We investigate the radix sort tree chains – the tree-valued Markov chains that arise when successively storing the finite collections of random infinite binary strings $Z_1,\ldots , Z_n$, $n=1,2,\ldots $ according to the trie-based radix sort algorithm, where the source strings $Z_1, Z_2,\ldots $ are independent and...

Evans, Steven N.; Wakolbinger, Anton
The trie-based radix sort algorithm stores pairwise different infinite binary strings in the leaves of a binary tree in a way that the Ulam-Harris coding of each leaf equals a prefix (that is, an initial segment) of the corresponding string, with the prefixes being of minimal length so that they are pairwise different. We investigate the radix sort tree chains – the tree-valued Markov chains that arise when successively storing the finite collections of random infinite binary strings $Z_1,\ldots , Z_n$, $n=1,2,\ldots $ according to the trie-based radix sort algorithm, where the source strings $Z_1, Z_2,\ldots $ are independent and...

Evans, Steven N.; Wakolbinger, Anton
The trie-based radix sort algorithm stores pairwise different infinite binary strings in the leaves of a binary tree in a way that the Ulam-Harris coding of each leaf equals a prefix (that is, an initial segment) of the corresponding string, with the prefixes being of minimal length so that they are pairwise different. We investigate the radix sort tree chains – the tree-valued Markov chains that arise when successively storing the finite collections of random infinite binary strings $Z_1,\ldots , Z_n$, $n=1,2,\ldots $ according to the trie-based radix sort algorithm, where the source strings $Z_1, Z_2,\ldots $ are independent and...

Evans, Steven N.; Wakolbinger, Anton
The trie-based radix sort algorithm stores pairwise different infinite binary strings in the leaves of a binary tree in a way that the Ulam-Harris coding of each leaf equals a prefix (that is, an initial segment) of the corresponding string, with the prefixes being of minimal length so that they are pairwise different. We investigate the radix sort tree chains – the tree-valued Markov chains that arise when successively storing the finite collections of random infinite binary strings $Z_1,\ldots , Z_n$, $n=1,2,\ldots $ according to the trie-based radix sort algorithm, where the source strings $Z_1, Z_2,\ldots $ are independent and...

Daly, Fraser
One major obstacle in applications of Stein’s method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the approximating compound Poisson random variable. In general, the best such bounds have an exponential dependence on these parameters, though in certain situations better bounds are available. In this paper, we extend the region for which well-behaved magic factors are available for compound Poisson approximation in the Kolmogorov metric, allowing useful compound Poisson approximation theorems to be established in some regimes where they were previously unavailable....

Daly, Fraser
One major obstacle in applications of Stein’s method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the approximating compound Poisson random variable. In general, the best such bounds have an exponential dependence on these parameters, though in certain situations better bounds are available. In this paper, we extend the region for which well-behaved magic factors are available for compound Poisson approximation in the Kolmogorov metric, allowing useful compound Poisson approximation theorems to be established in some regimes where they were previously unavailable....

Daly, Fraser
One major obstacle in applications of Stein’s method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the approximating compound Poisson random variable. In general, the best such bounds have an exponential dependence on these parameters, though in certain situations better bounds are available. In this paper, we extend the region for which well-behaved magic factors are available for compound Poisson approximation in the Kolmogorov metric, allowing useful compound Poisson approximation theorems to be established in some regimes where they were previously unavailable....

Daly, Fraser
One major obstacle in applications of Stein’s method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the approximating compound Poisson random variable. In general, the best such bounds have an exponential dependence on these parameters, though in certain situations better bounds are available. In this paper, we extend the region for which well-behaved magic factors are available for compound Poisson approximation in the Kolmogorov metric, allowing useful compound Poisson approximation theorems to be established in some regimes where they were previously unavailable....

Daly, Fraser
One major obstacle in applications of Stein’s method for compound Poisson approximation is the availability of so-called magic factors (bounds on the solution of the Stein equation) with favourable dependence on the parameters of the approximating compound Poisson random variable. In general, the best such bounds have an exponential dependence on these parameters, though in certain situations better bounds are available. In this paper, we extend the region for which well-behaved magic factors are available for compound Poisson approximation in the Kolmogorov metric, allowing useful compound Poisson approximation theorems to be established in some regimes where they were previously unavailable....

Bell, Denis; Nualart, David
We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Hermite processes $Z_\gamma $ with kernels defined by parameters $\gamma $ taking values in a tetrahedral region $\Delta $ of $\mathbb{R} ^q$. We prove that, as $\gamma $ converges to a face of $\Delta $, the process $Z_\gamma $ converges to a compound Gaussian distribution with random variance given by the square of a Hermite process of one lower rank. The convergence in law is shown to be stable. This work generalizes a previous result of Bai and Taqqu, who proved the result...

Bell, Denis; Nualart, David
We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Hermite processes $Z_\gamma $ with kernels defined by parameters $\gamma $ taking values in a tetrahedral region $\Delta $ of $\mathbb{R} ^q$. We prove that, as $\gamma $ converges to a face of $\Delta $, the process $Z_\gamma $ converges to a compound Gaussian distribution with random variance given by the square of a Hermite process of one lower rank. The convergence in law is shown to be stable. This work generalizes a previous result of Bai and Taqqu, who proved the result...

Bell, Denis; Nualart, David
We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Hermite processes $Z_\gamma $ with kernels defined by parameters $\gamma $ taking values in a tetrahedral region $\Delta $ of $\mathbb{R} ^q$. We prove that, as $\gamma $ converges to a face of $\Delta $, the process $Z_\gamma $ converges to a compound Gaussian distribution with random variance given by the square of a Hermite process of one lower rank. The convergence in law is shown to be stable. This work generalizes a previous result of Bai and Taqqu, who proved the result...

Bell, Denis; Nualart, David
We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Hermite processes $Z_\gamma $ with kernels defined by parameters $\gamma $ taking values in a tetrahedral region $\Delta $ of $\mathbb{R} ^q$. We prove that, as $\gamma $ converges to a face of $\Delta $, the process $Z_\gamma $ converges to a compound Gaussian distribution with random variance given by the square of a Hermite process of one lower rank. The convergence in law is shown to be stable. This work generalizes a previous result of Bai and Taqqu, who proved the result...

Bell, Denis; Nualart, David
We use techniques of Malliavin calculus to study the convergence in law of a family of generalized Hermite processes $Z_\gamma $ with kernels defined by parameters $\gamma $ taking values in a tetrahedral region $\Delta $ of $\mathbb{R} ^q$. We prove that, as $\gamma $ converges to a face of $\Delta $, the process $Z_\gamma $ converges to a compound Gaussian distribution with random variance given by the square of a Hermite process of one lower rank. The convergence in law is shown to be stable. This work generalizes a previous result of Bai and Taqqu, who proved the result...